The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A329001

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A329001

Numerator of the rational constant term c(n) of the n-th moment mu(n) of the limiting distribution of the number of comparisons in quicksort (for n >= 0).
(history; published version)

#67 by N. J. A. Sloane at Sun Mar 28 12:11:51 EDT 2021

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proposed

approved

#66 by Jean-François Alcover at Sun Mar 28 03:05:31 EDT 2021

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editing

proposed

#65 by Jean-François Alcover at Sun Mar 28 03:05:22 EDT 2021

MATHEMATICA

(* The function A is defined in A330852. *)

c[p_] := c[p] = Module[{v, a}, If[p == 0, v = 1; ]; If[p == 1, v = 0]; If[2 <= p, v = (p - 1)!*Sum[(-2)^(a + 1)*A[a + 1]*c[p - 1 - a]/(a!*(p - 1 - a)!), {a, 0, p - 1}]]; v];

Table[Numerator[c[n]], {n, 0, 15}] (* Jean-François Alcover, Mar 28 2021, after Maple code *)

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approved

editing

#64 by Joerg Arndt at Wed Jul 08 03:24:51 EDT 2020

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proposed

approved

#63 by Michel Marcus at Wed Jul 08 02:39:31 EDT 2020

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editing

proposed

#62 by Michel Marcus at Wed Jul 08 02:39:27 EDT 2020

LINKS

Kok Hooi Tan and Petros Hadjicostas, <a href="/A330852/a330852.pdf">Density and generating functions of a limiting distribution in quicksort</a>, Technical Report #568, Department of Statstics, Statistics, Carnegie Mellon University, Pittsburgh, PA, USA, 1993; see pp. 9-11.

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approved

editing

#61 by Peter Luschny at Sat Jul 04 15:59:17 EDT 2020

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proposed

approved

#60 by Petros Hadjicostas at Sat Jul 04 12:08:24 EDT 2020

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editing

proposed

#59 by Petros Hadjicostas at Sat Jul 04 12:08:16 EDT 2020

LINKS

Kok Hooi Tan and Petros Hadjicostas, <a href="https://doi.org/10.1016/0167-7152(94)00209-Q">Some properties of a limiting distribution in Quicksort</a>, Statistics and Probability Letters, 25(1), (1995, ), 87-94.

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proposed

editing

#58 by Petros Hadjicostas at Sat Jul 04 08:34:19 EDT 2020

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editing

proposed

Discussion

Sat Jul 04

08:34

Petros Hadjicostas: Typo...